11 research outputs found
Partial Stability Concept in Extremum Seeking Problems
The paper deals with the extremum seeking problem for a class of cost
functions depending only on a part of state variables of a control system. This
problem is related to the concept of partial asymptotic stability and analyzed
by Lyapunov's direct method and averaging schemes. Sufficient conditions for
the practical partial stability of a system with oscillating inputs are derived
with the use of Lie bracket approximation techniques. These conditions are
exploited to describe a broad class of extremum-seeking controllers ensuring
the partial stability of the set of minima of a cost function. The obtained
theoretical results are illustrated by the Brockett integrator and rotating
rigid body.Comment: This is the author's version of the manuscript accepted for
publication in the Proceedings of the Joint 8th IFAC Symposium on Mechatronic
Systems and 11th IFAC Symposium on Nonlinear Control Systems (MECHATRONICS &
NOLCOS 2019
On Exponential Stabilization of Nonholonomic Systems with Time-Varying Drift
A class of nonlinear control-affine systems with bounded time-varying drift
is considered. It is assumed that the control vector fields together with their
iterated Lie brackets satisfy Hormander's condition in a neighborhood of the
origin. Then the problem of exponential stabilization is treated by exploiting
periodic time-varying feedback controls. An explicit parametrization of such
controllers is proposed under a suitable non-resonance assumption. It is shown
that these controllers ensure the exponential stability of the closed-loop
system provided that the period is small enough. The proposed control design
methodology is applied for the stabilization of an underwater vehicle model and
a front-wheel drive car.Comment: This is the author's version of the manuscript accepted for
publication in the Proceedings of the Joint 8th IFAC Symposium on Mechatronic
Systems and 11th IFAC Symposium on Nonlinear Control Systems (MECHATRONICS &
NOLCOS 2019